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The $LRC$ circuit above is connected to an alternating voltage $V_0\sin(\omega t)$ and the circuit run until it is in a steady state.

1. Write Kirchoff's voltage rule for this circuit loop.
2. Draw the phasor diagram for the voltage, noting that the current must be in phase with the voltage across the resistor.
3. From this phasor diagram and the relations between maximum current, reactance or resistance of the circuit elements, and the maximum voltage drop across them, deduce and draw the phasor diagram for the impedance $Z$ of the circuit.
4. Draw a qualitatively correct figure of $P_{\rm av}(\omega)$ (the average power as a function of $\omega$) for the oscillator if it has $Q = 10$ and a resonant frequency $\omega_0$.